The center problem for analytic maps with mixed even-degree termsPetek, Renato (Avtor) Ferčec, Brigita (Avtor) Fernandes, Wilker (Avtor) Mencinger, Matej (Avtor) discrete dynamical systemscenter varietyanalytic mapsPoincaré return mapWe investigate the center problem for analytic maps implicitly defined by algebraic equations of the form F(x, y) = x + y + ∑ i+k=2αi,kxiyk = 0. Previous studies of homogeneous analytic maps of even degree and of mixed terms of degrees 2 and 4 revealed two recurring algebraic families characterizing the existence of a center at the origin: mirror-symmetry conditions and alternating-sum conditions. In this paper, we resolve the next open case involving mixed terms of degrees 2 and 6 and show that the same algebraic structure extends to mixed terms of degrees 2 and arbitrary even number. Using an approach based on the involutive identity f ( f (x)) = x, we prove that these two families of algebraic conditions completely characterize the existence of a center at the origin. The proof combines algebraic and structural arguments and avoids the use of explicit higher-order focus quantity computations in the general case.MDPI20262026-09-21 10:26:16Članek v reviji100500UDK: 517.9COBISS_ID: 291745027DOI: 10.3390/axioms15090669ISSN pri članku: 2075-1680sl